Time Limit: 2 second(s) | Memory Limit: 32 MB |
You are in a maze; seeing n doors in front of you in beginning. You can choose any door you like. The probability for choosing a door is equal for all doors.
If you choose the i^{th} door, it can either take you back to the same position where you begun in x_{i} minutes, or can take you out of the maze after x_{i} minutes. If you come back to the same position, you can't remember anything. So, every time you come to the beginning position, you have no past experience.
Now you want to find the expected time to get out of the maze.
Input starts with an integer T (≤ 100), denoting the number of test cases.
Each case contains a blank line and an integer n (1 ≤ n ≤ 100) denoting the number of doors. The next line contains n space separated integers. If the i^{th} integer (x_{i}) is positive, you can assume that the i^{th} door will take you out of maze after x_{i} minutes. If it's negative, then the i^{th} door will take you back to the beginning position after abs(x_{i}) minutes. You can safely assume that 1 ≤ abs(x_{i}) ≤ 10000.
For each case, print the case number and the expected time to get out of the maze. If it's impossible to get out of the maze, print 'inf'. Print the result in p/q format. Where p is the numerator of the result and q is the denominator of the result and they are relatively prime. See the samples for details.
Sample Input |
Output for Sample Input |
3
1 1
2 -10 -3
3 3 -6 -9 |
Case 1: 1/1 Case 2: inf Case 3: 18/1 |
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